The Hermitian Solution to a New System of Commutative Quaternion Matrix Equations
Yue Zhang, Qing‐Wen Wang, Lv-Ming Xie
Abstract
This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, where we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. In addition, we also provide the least squares Hermitian solution in cases where the system of matrix equations is not consistent. To illustrate our main findings, in this paper we present two numerical algorithms and examples.
Topics & Concepts
QuaternionHermitian matrixCommutative propertyMathematicsMatrix (chemical analysis)System of linear equationsPure mathematicsHermitian functionExpression (computer science)Applied mathematicsAlgebra over a fieldMathematical analysisComputer scienceGeometryProgramming languageMaterials scienceComposite materialMatrix Theory and AlgorithmsAlgebraic and Geometric AnalysisElectromagnetic Scattering and Analysis